[R-lang] Re: Concerning glm with contrasts
Levy, Roger
rlevy@ucsd.edu
Thu Jul 22 18:53:17 PDT 2010
On Jul 21, 2010, at 9:58 AM, Zoe Luk wrote:
> Dear Dr. Levy,
>
> Thank you very much for your detailed response. Your information is very helpful.
No problem, Zoe -- my follow-ups are below.
>
> Here are my answers to your questions, and I have some further questions below.
> 1) The totals are all 508 for all languages because I want to make sure that I am comparing the frequencies of constructions that are conveying the same meanings. The counts are based on a novel which is originally written in Japanese, and translated into Chinese and English. When I analyzed the texts, I only included those that have equivalents in all three languages. Therefore, they always have the same totals. I guess then the totals are not something that I'm interested in. I'm interested in how the languages differ in terms of the frequencies of different constructions.
Yes, this makes a lot of sense and you clearly are not interested in the marginal counts in this case (though I guess that in principle you could have had a slightly different number of clauses in each language depending on the translation).
> 2) The reason I used Poisson is because I thought it is appropriate for count data. Also I have a friend who is a statistician, and this is her suggestion.
You're right -- it *is* appropriate for count data, and it's perfect, but my personal experience is that the interpretation of the Poisson formulation often comes a little less naturally to people than the interpretation of the (multinomial) logistic regression formulation. Technically, the way you're using the Poisson model is what's called "surrogate Poisson" -- you're using Poisson regression to model what are actually multinomial frequencies. Venables & Ripley section 7.3 has some discussion of this.
> 3) Regarding Q3 in my original post, my hypothesis is that English prefers passive more than Japanese does, and Japanese prefers Intransitive more than English, but Chinese can be either in both cases.
OK (though I'm not sure I understood the last part regarding Chinese) -- but does "prefer passive" simply mean that a larger proportion of the clauses are passive in English than in Japanese? Likewise for intransitive.
> Here are my further questions:
> 1) You mentioned "multinominal logistic regression". I do know a little about logistic regression, but not at all about this specific kind of logistic regression. Which command should I use? glm(), mlogit(), lmer(), or something else? And what kind of distribution (e.g., binomial) should I use?
There are a few options, including the "multinom" function in the nnet package, and the "multinomial" function in the VGAM package. If you wind up interested in mixed-effects models, some people have ben using the MCMCglmm package.
> 2) Regarding the significant difference shown in "language1" in the model, you said that "the language1 variable more or less models the relative frequency of English observations to Japanese observations". I am not sure I am following. So what can I claim (or what do I know) based on this result?
Given the way you have collected your data and set up your model, you would not be interested in the values of the intercept or the language parameters -- it's the construction and construction/language interaction parameters that matter. But the way you've coded your contrasts makes the interpretation difficult; for the hypotheses you're interested in, I suggest you think about using "treatment" coding rather than the sum contrast coding that your original post had.
> 3) As mentioned above, I do not have a specific hypothesis for Chinese. If I want to include it in the analysis anyway (e.g., comparing passive constructions in all three languages), what methods would you advise me to use?
Well, I think it would depend on what underlying assumptions you have (e.g., do you implicitly think that Chinese is likely to be similar to English and Japanese overall, and so somehow including Chinese data would help you interpret the English & Japanese counts more reliably?). If you have no hypotheses regarding Chinese at the moment, you might just consider not including those data in the analysis at this point.
Best
Roger
>
> Thank you in advance, and I look forward to hearing from you.
>
> Regards,
> Zoe
>
> On Tue, Jul 20, 2010 at 4:43 PM, Levy, Roger <rlevy@ucsd.edu> wrote:
> Dear Zoe,
>
> On Jul 19, 2010, at 10:28 AM, Zoe Luk wrote:
>
> > Dear R-lang users,
> >
> > I am new to the mailing list, and also rather new to R. I have a few questions concerning the results of glm().
> >
> > I am doing a study comparing the frequencies of different linguistic constructions used in a specific text that is in three languages (Japanese, Chinese, and English). The results I got are the following.
> >
> >
> > Transitive Passive Intransitive Adjectival Others Total
> > Japanese 164 9 291 36 8 508
> > Chinese 198 3 221 69 17 508
> > English 174 31 214 57 32 508
> >
> > 536 43 726 162 57 1524
> >
> > Chi-square test has a significant result. I intended to do further analysis to see if there is any difference among the languages, so i did the following:
> >
> > > glm.out4<-glm(freq~language*constructions, data=comps2.data, family=poisson, contrasts=list(language=contrastml, constructions=contrastmc))
>
> The first question I'd like to ask is why you're using a Poisson model to analyze your data. I see that the marginal totals for each language are the same at 508. Were these marginal totals under your control (e.g., did you count in each text until you got 508), or are these totals something you want your model to account for? A Poisson model devotes parameters to accounting for the marginal totals. If instead you're thinking that the language is an "independent variable" and the construction type is a "dependent variable", then analyzing the data with multinomial logistic regression might be more appropriate. (Now, there *are* legitimate uses of Poisson models as surrogates for multinomial logistic regression, but using them in surrogates in this way affects how you interpret the model parameters -- see below.)
>
> > > summary(glm.out4)
> >
> > Call:
> > glm(formula = freq ~ language * constructions, family = poisson,
> > data = comps2.data, contrasts = list(language = contrastml,
> > constructions = contrastmc))
> >
> > Deviance Residuals:
> > [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> >
> > Coefficients:
> > Estimate Std. Error z value Pr(>|z|)
> > (Intercept) 3.93111 0.05890 66.746 < 2e-16 ***
> > language1 0.20443 0.08435 2.424 0.015363 *
> > language2 0.16064 0.09497 1.692 0.090740 .
> > constructions1 -1.25129 0.06779 -18.459 < 2e-16 ***
> > constructions2 1.68783 0.18775 8.990 < 2e-16 ***
> > constructions3 -0.01655 0.08647 -0.191 0.848205
> > constructions4 1.12805 0.13321 8.468 < 2e-16 ***
> > language1:constructions1 0.12190 0.09726 1.253 0.210090
> > language2:constructions1 0.26651 0.10562 2.523 0.011625 *
> > language1:constructions2 0.15838 0.24722 0.641 0.521744
> > language2:constructions2 -0.98403 0.32782 -3.002 0.002684 **
> > language1:constructions3 -0.15971 0.12915 -1.237 0.216218
> > language2:constructions3 0.44708 0.12620 3.543 0.000396 ***
> > language1:constructions4 -0.51918 0.21538 -2.411 0.015931 *
> > language2:constructions4 0.19079 0.18724 1.019 0.308207
> > ---
> > Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> >
> > (Dispersion parameter for poisson family taken to be 1)
> >
> > Null deviance: 1.3744e+03 on 14 degrees of freedom
> > Residual deviance: -3.1086e-15 on 0 degrees of freedom
> > AIC: 116.66
> >
> > Number of Fisher Scoring iterations: 3
> >
> > > contrasts(language)
> > [,1] [,2]
> > Chinese 0 -1
> > English 1 1
> > Japanese -1 0
> > > contrasts(constructions)
> > [,1] [,2] [,3] [,4]
> > Adjectival 0 0 -1 0
> > Intransitive 1 1 1 1
> > Others 0 0 0 -1
> > Passive 0 -1 0 0
> > Transitive -1 0 0 0
> >
> > So my questions are:
> > (1) I am not sure how to interpret these results. Since language1 shows a significance difference, does it mean that "English and Japanese are significantly different in terms of the distribution of the different constructions used"?
>
> No -- since you're using Poisson regression, the language1 variable more or less models the relative frequency of English observations to Japanese observations.
>
> If you were to double the number of observations in each Japanese cell, the biggest change in your model would be that the language1 parameter would decrease. (The intercept and the language2 parameter would also adjust by smaller amounts, in compensation.) The constructions and language:constructions parameters would stay the same
>
> > (2) Does the "intercept" represent anything at all? If yes, what does it represent in this case?
>
> It probably not anything you're interested in. Because you're using true contrasts (i.e. each column in your contrast matrices sums to zero), the intercept is more or less modeling the total number of observations in your dataset (keep in mind that Poisson regression is trying to model cell counts, not proportions).
>
> If you were to double the counts of all cells in your dataset, the intercept would increase by a constant factor -- log(2) -- and the rest of the model would stay the same.
>
> > (3) If I want to test whether English uses passive significantly more than Japanese, and Japanese uses intransitive significantly more than English, how should I modify the contrasts/commands?
>
> Let's call the passive question 3a, and the intransitive question 3b. Answering these question depends on the answers to a couple of other questions:
>
> * How, if at all, are the Chinese data relevant to either 3a or 3b?
>
> * How, if at all, are the distinctions among adjectival, intransitive, transitive, and "other" relevant to 3a?
>
> * How, if at all, are the distinctions among adjectival, passive, transitive, and "other" relevant to 3b?
>
> If the answer to all three questions is "irrelevant", you might just consider doing very simple chi-squared or Fisher's exact tests on 2x2 representations of the Japanese and English as (a) passive and non-passive counts, and (b) intransitive and non-intransitive counts.
>
> Also, I'd recommend Maureen Gillespie's coding tutorial as background reading:
>
> http://go2.wordpress.com/?id=725X1342&site=hlplab.wordpress.com&url=http%3A%2F%2Fhlplab.files.wordpress.com%2F2010%2F05%2Fcodingtutorial.pdf&sref=http%3A%2F%2Fhlplab.wordpress.com%2F2010%2F05%2F10%2Fmini-womm-montreal-slides-now-available%2F
>
> Best
>
> Roger
>
> --
>
> Roger Levy Email: rlevy@ling.ucsd.edu
> Assistant Professor Phone: 858-534-7219
> Department of Linguistics Fax: 858-534-4789
> UC San Diego Web: http://ling.ucsd.edu/~rlevy
>
>
>
>
>
>
>
>
>
>
> --
> Zoe Luk
> Department of Linguistics
> University of Pittsburgh
>
>
--
Roger Levy Email: rlevy@ling.ucsd.edu
Assistant Professor Phone: 858-534-7219
Department of Linguistics Fax: 858-534-4789
UC San Diego Web: http://ling.ucsd.edu/~rlevy
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